Principal of duality
One expression can be obtain from another expression by replacing the every 1 with 0, every 0 with 1, every (+) with (.), every (.) with (+). Any pair of expression satisfying this property is called dual expression. This characteristic of Boolean algebra is called the principle of duality.
Two important theorems are proposed by DeMorgan. This two theorems have very important role in Boolean expression.
Theorem I: The Complement of a product is equal to the sum of the complements.
A.B = A + B
Theorem II: The Complement of a sum is equal to the product of the complements.
A + B = A . B
Proof for DeMorgan’s theorems
|A||B||A||B||A+B||A.B||A+B||A . B||A . B||A + B|